Question 50472: factor the following:
1)x squared + 6x + one
2)x squared + 8x + 2
3)x squared - 8 - 5
4)x squared + 12 x + twenty-one
5)x squared + 3 x + 3/2[-1/2, 2]
6)x squared - 2 x + 1/2
7)x to the power of four + 16y
8)4x to the power of four + y to the power of four
9)16x to the power of four z + 4z to the power of five
10)10xz to the power of four + 40x
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website! The first seven cannot be factored, but the last
three can be:
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8)4x to the power of four + y to the power of four
4x4 + y4
Add and subtract 4x2y2
4x4 + 4x2y2 + y4 - 4x2y2
The first three terms can be factored as a perfect square, and
the last term is itself a perfect square.
(2x2 + y2)2 - (2xy)2
This is the difference of two perfect squares:
[(2x2 + y2) - 2xy][(2x2 + y2) + 2xy]
Get rid of unnecessary grouping symbols:
(2x2 + y2 - 2xy)(2x2 + y2 + 2xy)
Arrange in descending powers of x and ascending
powers of y
(2x2 - 2xy + y2)(2x2 + 2xy + y2)
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9)16x to the power of four z + 4z to the power of five
16x4z + 4z
Factor out GCF 4z
4z{4x4 + 1}
Add and subtract 4x2 in the braces
4z{4x4 + 4x2 + 1 - 4x2}
The first three terms in braces can be factored as a
perfect square, and the last term is itself a perfect
square.
4z{(2x2 + 1)2 - (2x)2}
The expression in braces is the difference of two
perfect squares
4z{[(2x2 + 1) - (2x)][(2x2 + 1) + (2x)]
Get rid of unnecessary grouping symbols
4z(2x2 + 1 - 2x)(2x2 + 1 + 2x)
Arrange the expressions in parentheses in descending
order of x
4z(2x2 - 2x + 1)(2x2 + 2x + 1)
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10)10xz to the power of four + 40x
10xz4 + 40x
Factor out GCF 10x
10x{z4 + 4}
Add and subtract 4z2 in the braces
10x{z4 + 4z2 + 4 - 4z2}
The first three terms in braces can be factored as a
perfect square, and the last term is itself a perfect
square.
10x{(z2 + 2)2 - (2z)2}
The expression in braces is the difference of two
perfect squares
10x{[(z2 + 2) - (2z)][(z2 + 2) + (2z)]
Get rid of unnecessary grouping symbols
10x(z2 + 2 - 2z)(z2 + 2 + 2z)
Arrange the expressions in parentheses in descending
order of z
10x(z2 - 2z + 2)(z2 + 2z + 2)
Edwin
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